本研究決策情境為單一供應商將耗損性產品送給多個零售商之供應鏈體系中，來探討供應商和零售商彼此之間的補貨問題。本研究的決策變數分別為：零售商之補貨週期T及運送頻率 ；即期望透過零售商的補貨週期及運送頻率，降低整體供應鏈的平均總成本。在理論分析的探討中，我們首先推導出由供應商和所有零售商所組成的聯合總平均成本，接下來再針對聯合總平均成本曲線的最佳解結構特性進行探討。其中我們證明得到聯合總平均成本函數對時間T具有片段凹性的性質。同時，我們針對聯合總平均成本曲線的最佳解位置，接合點及區域最低值的發生點做探討。上述之理論分析的結果，將有助於提出有效的搜尋演算法，求取本模式的最佳解。論文中也將舉範例與多個隨機實驗之數據來驗證並說明本研究中所得之理論結果，且隨機實驗結果比Yang 與Wee (2000)好。 In this paper, we consider an integrated inventory model with one vendor and multiple buyers with deteriorating products by deriving a new approximation function. In this supply chain, the vendor purchases raw materials, and immediately produces into finished items, and delivers finished items to multiple buyers. In order to solve this problem, we explore the optimality structure and derive several interesting properties on the curve of optimal objective function value with respect to T. By utilizing our theoretical results, we propose a search algorithm that can efficiently solves the optimal solution with respect to the value of sorted setup of junction point W. We derive an upper bound and a lower bound as the search range. Based on our numerical experiments, we show that our search algorithm secures the optimal solution in a very short run time. We also shown that the proposed search algorithm is more efficient than Yang and Wee’ algorithm.
